I have been reading two highly interesting articles by Robert Kiehn. The first article has the title "Hydrodynamics wakes and minimal surfaces with fractal boundaries". Second article is titled "Instability patterns, wakes and topological limit sets". There are very many contacts on TGD inspired vision and its open interpretational problems.

The notion of Falaco soliton has surprisingly close resemblance with Kähler magnetic flux tubes defining fundamental structures in TGD Universe. Fermionic strings are also fundamental structures of TGD accompanying magnetic flux tubes and this supports the vision that these string like objects could allow reduction of various condensed matter phenomena such as sound waves -usually regarded as emergent phenomena allowing only highly phenomenological description - to the fundamental microscopic level in TGD framework. This can be seen as the basic outcome of reading the articles.

Kiehn proposed a new description for the generation of various instability patterns of hydrodynamics flows (Kelvin-Helmholtz and Rayleigh-Taylor instabilities) in terms of hyperbolic dynamics so that a connection with wave phenomena like interference and diffraction would emerge. The role of characteristic surfaces as surfaces of tangential and also normal discontinuities is central for the approach. In TGD framework the characteristic surfaces have as analogs light-like wormhole throats at which the signature of the induced 4-metric changes and these surfaces indeed define boundaries of two phases and of material objects in general. This inspires a more detailed comparison of Kiehn's approach with TGD.

For details see the article Robert Kiehn's ideas about Falaco solitons and generation of turbulent wake from TGD perspective.

## 5 comments:

Dear Matti,

The speed of progress of TGD is more than me about learning of TGD ;-).

“One identification for the space-time representative of macroscopic objects is as the analog of line of Feynman diagram, which is space-time region with Euclidian signature.”

We see macroscopic objects as 2-surfaces that are boundary of 3-surfaces. So the space-time representative of macroscopic objects is the 2-surfaces that are evolving in larger space-time sheet. I deduce from your sentence that the evolving for the 2-surfaces have Euclidian signature. This is inconsistent with what I understand from special relativity. I think I misunderstood your sentence.

In path integral formalism, what is physical Intuition behind wick rotation? In QFT it is only a mathematical tool. What is about TGD?

I myself, intermix the quantum and classical together. Ye, it is unavoidable;-). Sorry for my request in some comment ago. Obviously you know very better how to say about TGD.

Dear Hamed,

here are my comments.

[Hamed]

?One identification for the space-time representative of macroscopic

objects is as the analog of line of Feynman diagram, which is space-time

region with Euclidian signature.?

[MP] This is ok. An alternative identification of generalized Feynman diagram is as the light-like wormhole throat at which the signature changes since one can assign quantum numbers to this region.

[Hamed] We see macroscopic objects as 2-surfaces that are boundary of 3-surfaces.

So the space-time representative of macroscopic objects is the 2-surfaces

that are evolving in larger space-time sheet. I deduce from your sentence

that the evolving for the 2-surfaces have Euclidian signature. This is

inconsistent with what I understand from special relativity. I think I

misunderstood your sentence.

[MP] Evolving 2-surfaces define 3-D light-like wormhole throat orbits since they have have neither Minkowskian nor Euclidian signature and thus have degenerate signature of 4-metric: 4-D tangent space of space-time surface becomes metrically 3-D at the orbit of wormhole throat. All boundaries between various objects have this character.

TGD of course generalizes dramatically the views of special relativity and general relativity about space-time. In special relativity one has just M^4: in TGD it is replaced with imbedding space M^4xCP_2 so that symmetries are not lost. In general relativity one allows only Minkowskian signature. In TGD one allows both signatures. This is rather radical departure.

[Hamed] In path integral formalism, what is physical Intuition behind wick

rotation? In QFT it is only a mathematical tool. What is about TGD?

I myself, intermix the quantum and classical together. Ye, it is

unavoidable;-). Sorry for my request in some comment ago. Obviously you

know very better how to say about TGD.

[MP] I see Wick rotation as a pure mathematical trick analogous to analytic continuation allowing to make the four-dimensional loop momentum integrals well-defined in QFT. In twistor Grassmannian approach the idea is a kind of residue calculus: the loop integrals can be reduced so one obtains only integrals over massless on mass-shell virtual momenta which can be however complex: they are expressed in terms of twistor variables. In the similar manner integral of analytic functions over real axis can be expressed in terms of residues at poles in either upper or lower complex plane.

I remember vaguely that I have considered the possibility of Wick rotation in the proposal for how the space-time surfaces could be seen as (in some sense) quaternionic sub-manifolds of octonionic M^8: for this option I considered octonion real analytic functions and put imaginary part of the function to zero to define a four-surface. In complex plane the vanishing of a complex function defines a curve. At this moment I am not too enthusiastic about this kind of approach although it would provide general solution of field equations by M^8-M^4\times CP_2 correspondence.

We experience the world as classical and proper quantum theory must explain this. The challenge is not to eliminate fuzzy quasiclassical arguments from the theory but make classical physics a precise part of the theory. And classical physics as exact part of quantum physics follows from single principle: general coordinate invariance realized at the level of WCW. GCI implies immediately holography, even in strong form. "Bohr orbitology" follows as by product of general coordinate invariance. All this demonstrates the amazing power of GCI: the great principles of Einstein transcend much beyond GRT.

Dear Matti

Falaco-soliton demonstrated by Kiehn in swimming pool hides his "wormhole" which is clearly visible in porridge-containing dishwater. Could the photon be minimal topological defect, Falaco-soliton? Two against each other colliding Falaco-solitons in water expel each other. It is probable that opposite solitons (in vacuum) should bring them closer.

I regret to inform everyone that my longtime friend, Robert Kiehn, passed away yesterday. He was a heroic figure, wonderful father and a great friend to all.

My deep condolences. For years ago we were in interaction and had email discussions about topological thermodynamics. Robert's work was intellectually very stimulating.

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